Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#121×C53 ⋊ C4 |
| Sylow | C53 ⋊ #10971 |
1630 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=g,d^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^30,c^b=cf,d^b=dh,i^g=i^52428 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1092676);